Electronic correlations versus lattice interactions: Interplay of charge and anion orders in ${\left(\mathrm{TMTTF}\right)}_{2}X$

The quasi-one-dimensional molecular conductors ${\left(\mathrm{TMTTF}\right)}_{2}X$ commonly undergo a charge-order transition upon cooling. For tetrahedral anions ($X={\mathrm{BF}}_4^{-}, {\mathrm{ClO}}_4^{-}$, and ${\mathrm{ReO}}_4^{-}$), in addition, anion ordering is observed. In a comprehensive infrared study, we trace the resonance frequencies of the charge-sensitive vibrational modes to determine the charge disproportionation $2\delta ={\rho }_{\mathrm{rich}}-{\rho }_{\mathrm{poor}}$ as a function of temperature. In combination with analog investigations for the centrosymmetric anions, we conclude that charge order does not depend on the anion shape and symmetry, but is intrinsic to the TMTTF stack. Since correlation effects are of paramount importance, we find a universal relation between the charge imbalance $2\delta$ and ordering temperatures $T_{\mathrm{CO}}$ and gaps ${\mathrm{\Delta }}_{\mathrm{CO}}$, respectively. Below $T_{\mathrm{AO}}$ the charge disproportionation gradually changes. Ordering of the tetrahedral anions minimizes the electrostatic energy for the anions and organic molecules as a whole, resulting in a 0110 pattern. This way we can understand that deuteration of the methyl end groups enhances $T_{\mathrm{CO}}$ but does not affect the anion ordering, which is linked to the anion-sulfur distance.

Figure 1

Crystal structure of ${\left(\mathrm{TMTTF}\right)}_{2}X$, where TMTTF stands for tetramethyltetrathiafulvalene and $X$ denotes a monovalent anion. (a) In the normal state the organic molecules experience a finite dimerization within the chain, with intra- and inter-dimer distances $d_1<d_2$, respectively. Between the TMTTF stacks the anions can freely rotate around their center position, as indicated by the green spheres. (b) At low temperatures the anions become ordered in an alternating fashion with wave vector $(1/2,1/2,1/2)$, causing a periodic modulation of the electrostatic potential along all three crystal directions. Under high pressure and in ${\left(\mathrm{TMTSF}\right)}_{2}X$ compounds the wave vector is different. The unit cell is doubled, now containing four inequivalent molecules; pairs of dimers separated by $d_2^{{}^{\prime \prime }}<d_2^{{}^{\prime }}$ imply a tetramerization of the organic molecules. Two molecules have close links to anions, two of them do not.

Figure 2

Temperature-dependent electrical resistivity of ${\left(\mathrm{TMTTF}\right)}_2{\mathrm{ReO}}_4, {\left(\mathrm{TMTTF}\right)}_2{\mathrm{BF}}_4$, and ${\left(\mathrm{TMTTF}\right)}_2{\mathrm{ClO}}_4$ measured along the chain direction. For clarity reasons the curve of ${\left(\mathrm{TMTTF}\right)}_2{\mathrm{BF}}_4$ is shifted down by a factor of 100. In order to illustrate the behavior around the anion transition temperature $T_{\mathrm{AO}}$, the respective resistivities are plotted during cooling (solid symbols) and warming (open symbols).

Figure 3

(a)–(c) Temperature evolution of the charge-sensitive infrared-active mode ${\nu }_{28}$ of ${\left(\mathrm{TMTTF}\right)}_{2}X$ with tetrahedral anions $X$ measured for $E\parallel c$. (d)–(f) At the charge-order transition the band splits into two peaks as a result of differently charged organic molecules. (g)–(i) According to Eq. (1), the charge disproportionation $2\delta =\mathrm{\Delta }\nu /(80{\mathrm{cm}}^{-1}/e)$ can be directly extracted from the peak separation $\mathrm{\Delta }\nu$. While in ${\left(\mathrm{TMTTF}\right)}_2{\mathrm{BF}}_4$ the mode splitting seems to be reduced below $T_{\mathrm{AO}}$, for ${\left(\mathrm{TMTTF}\right)}_2{\mathrm{ReO}}_4$ a strong enhancement sets in at the anion-ordered phase implying a further charge redistribution. Surprisingly, at $T_{\mathrm{AO}}$ there is also a splitting for $X={\mathrm{ClO}}_4^{-}$ in absence of electronically driven charge order.

Figure 4

(a) Charge imbalance related with electronically driven charge order as a function of transition temperature $T_{\mathrm{CO}}$ for ${\left(\mathrm{TMTTF}\right)}_{2}X$ with octahedral (open circles; Refs. [14, 16]) and tetrahedral (solid dots; this work) anions. The charge disproportionation of the different compounds follows one line, where the best fit was achieved for $2{\delta }_{\mathrm{CO}}\propto T_{CO}^{2/3}$ (red line). For completeness reasons, NMR [22, 43, 44] and Raman [15, 42] values are indicated by green crosses and plus signs, respectively. Infrared-active molecular vibrations, however, are the most direct and precise tool to determine the molecular charge. (b) Charge disproportionation plotted versus the charge order gap obtained from dc transport [5, 16]. $2{\delta }_{\mathrm{CO}}$ depends linearly on ${\mathrm{\Delta }}_{\mathrm{CO}}$. The CO gap could not be extracted accurately for small $T_{\mathrm{CO}}$ as indicated by the gray area.

Figure 5

Sketch of the molecular charge and anion arrangement in ${\left(\mathrm{TMTTF}\right)}_{2}X$ compounds at different temperatures. (a) While the stacks are dimerized at elevated temperatures, (b) the molecules are more equidistant with alternating charge-poor and charge-rich sites in the charge-ordered state. (c) The low-temperature ground state of ${\left(\mathrm{TMTTF}\right)}_{2}X$ with tetrahedral anions, however, is determined by ordering of the anions. Organic molecules with a ligand-sulfur short link acquire more positive charge.

Figure 6

The totally symmetric intramolecular ${\nu }_4\left({\mathrm{a}}_{\mathrm{g}}\right)$ mode is Raman-active and typically observed by infrared spectroscopy only as the out-of-phase vibration within a dimer. Tetramerization enables the combination of dimeric vibrations. Following common spectroscopic notation, the indices $x$ and $y$ stand for the symmetry ($g$ for in-phase, $u$ for out-of-phase) of the vibration within and between the two dimers, respectively. In particular, AO activates the dimeric in-phase vibration by out-of-phase combination of two dimers within the tetramer; the ${\nu }_{4,gu}$ mode couples to infrared light via the oscillating dipole $p$ (green arrow) between the dimers. Due to large wave function overlap between the charge-rich molecules in the center of the tetramer, the 0110 charge pattern increases vibrational coupling between the dimers resulting in enhanced intensity.

Figure 7

(a)–(c) When cooling below $T_{\mathrm{AO}}$, the tetrameric $v_{4,gu}$ mode depicted in Fig. 6 appears around $1410–1420{\mathrm{cm}}^{-1}$ providing evidence for the tetramerization of TMTTF molecules in the AO state. The data are vertically shifted for better illustration. (d) The integrated spectral weight of this mode scales with anion size and continuously grows upon cooling. Renormalization to the transition temperature and low-temperature intensity (inset) results in similar, mean-field-like curves for all compounds.

Figure 8

(a) Deuteration of the methyl end groups enhances charge ordering in ${\left(\mathrm{TMTTF}\right)}_{2}X$ (data taken from Refs. [20] and [56]) while $T_{\mathrm{AO}}$ remains unchanged. The stack dimerization is reduced. The change of transition temperature $\mathrm{\Delta }{T}_{\mathrm{CO}}$ is largest for small anions and small $T_{\mathrm{CO}}$. (b) The deuteration effect on CO can be described as a constant value $D$ that adds in quadrature to $T_{\mathrm{CO}}$. (c) The interaction of anions and TMTTF molecules that causes dimerization takes place via the hydrogen bonds; if dimerization diminishes, $T_{\mathrm{CO}}$ is enhanced. (d) Since AO is mainly affected by the interaction with the molecular charge, which scales with the shortest ligand-sulfur distance, deuteration has no influence on $T_{\mathrm{AO}}$.